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Chapter 4: Q. 65 (page 195)

In Problems 65鈥�68, construct a polynomial function that might have the given graph. (More than one answer may be possible.)

Short Answer

Expert verified

The possible function isf(x)=x(x-1)(x-2)

Step by step solution

01

Step 1. Given information

The graph is

02

Step 2. To find the possible function from graph.

In the given graph we can see that there are 3 zeros because the graph is crossing the x-axis at three different points:

x=0x=1x=2

So the factors of the function are: role="math" localid="1646318209936" x-0,x-1,x-2

At all these points the graph crosses x-axis

So each zero will have odd multiplicity

Hence the function is

f(x)=x(x-1)(x-2)

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Most popular questions from this chapter

Solve the inequality x2-5x鈮�24. Graph the solution set.

In Problems 25鈥�30, use the graph shown to find

(a) The domain and range of each function

(b) The intercepts, if any

(c) Horizontal asymptote, if one exists

(d) Vertical asymptotes, if any

(e) Oblique asymptote, if one exists

The illustration shows the graph of a polynomial function.

(a) Is the degree of the polynomial even or odd?

(b) Is the leading coefficient positive or negative?

(c) Is the function even, odd, or neither?

(d) Why is x2necessarily a factor of the polynomial?

(e) What is the minimum degree of the polynomial?

(f) Formulate five different polynomial functions whose

graphs could look like the one shown. Compare yours to those of other students. What similarities do you see?

What differences?

True or False. The graph of a rational function may intersect

a horizontal asymptote.

Find the real zeros of f. Use the real zeros to factor f. f(x)=x4+x3-3x2-x+2
See all solutions

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